Question

Use the given information to solve for x and find the indicated angle measure: Given m∠ADC = 135º, solve for x and find m∠BDC

Answer 1

Given
`\( m∠ADC = 135º \` ), to solve for
`\( x \)` , we use the fact that angles in a straight line add up to
`\( 180º \)` . Therefore,
`\( m∠BDC = 45º \).`

Step-by-step explanation:

In the context of the problem,
`\( ∠ADC \)` and
`\( ∠BDC \)` form a straight line. According to the angle sum property of a straight line, the sum of the measures of angles in a straight line is
`\( 180º \).` Therefore, to find
`\( m∠BDC \),` we subtract
`\( m∠ADC \)` from
`\( 180º \)` :
`\( m∠BDC = 180º - m∠ADC \).` Substituting the given value,
`\( m∠BDC = 180º - 135º = 45º \).`

This result is consistent with the fact that
`\( ∠ADC \)` and
`\( ∠BDC \)` are supplementary angles. Supplementary angles add up to
`\( 180º \),` and in this case, the measure of
`\( ∠BDC \)` complements
`\( ∠ADC \)` to form a straight line. The calculation
`\( m∠BDC = 180º - m∠ADC \)` is a fundamental application of angle properties and provides the angle measure
`\( m∠BDC \)` that completes the solution to the problem.

Understanding angle properties and applying them to geometric configurations is crucial in solving problems involving angle measures. In this case, recognizing the supplementary relationship between
`\( ∠ADC \)` and
`\( ∠BDC \)` allows us to determine the measure of
`\( ∠BDC \)` using the given information.